I just received the Mortarboard badge and create tag synonyms privilege - both of which I (regrettably) don't deserve. I have not earned 200 reputation on any day, and I have only 2318 reputation at the moment.

1 Answer
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The most likely scenario is that you got a surge of upvotes on your posts. This would trigger you to hit the reputation cap, and since you are less than 200 shy of the "create tag synonyms" privilege, that would put you at sufficient reputation for that. However, if all of these upvotes came from the same individual, then such an immediate and short-notice voting spree would be reverted (targeted upvoting is considered vote fraud of a sort, handled the same way for maliciously targeted downvoting). The Mortarboard badge fires off earlier than other badges, so it is possible to earn it before the votes are retracted.

With the exception of the tag specialist badges, badges do not get rescinded if you no longer satisfy the criteria. Likewise, the banner for reputation privileges is simply fired off without a mechanism to "undo" if you fall below the necessary threshold. This is what would let them persist until you return at a much later time to discover them in spite of the lack of evidence to either occurrence.